Area & Perimeter Word Problems worksheet for Grade 5 students.

I'll solve each problem step by step, checking my calculations carefully.

Problem 1:
The perimeter of a rectangular playground is 36 m. The length is 6 m. What is the width?

For a rectangle: Perimeter = 2 × (length + width)
36 = 2 × (6 + width)
36 = 12 + 2 × width
36 - 12 = 2 × width
24 = 2 × width
width = 24 ÷ 2 = 12 m

Let me verify: Perimeter = 2 × (6 + 12) = 2 × 18 = 36 ✓

Problem 2:
A rectangular room measures 15 m by 7 m. What is the area?

Area of rectangle = length × width
Area = 15 × 7 = 105 square meters

Let me verify: 15 × 7 = 105 ✓

Problem 3:
Emily's room is 12 ft by 12 ft. How much carpeting does she need?

This asks for the area to cover the entire floor.
Area = 12 × 12 = 144 square feet

Let me verify: 12 × 12 = 144 ✓

Problem 4:
Oliver wants to add a border around a 9 ft by 12 ft bulletin board. What is the length of the border?

The border goes around the entire edge, so we need the perimeter.
Perimeter = 2 × (length + width)
Perimeter = 2 × (9 + 12)
Perimeter = 2 × 21 = 42 ft

Let me verify: 2 × (9 + 12) = 2 × 21 = 42 ✓

Problem 5:
A flower garden is 5 meters long and 12 meters wide. One bag covers 5 square meters. How many bags needed?

First, find the area:
Area = 5 × 12 = 60 square meters

Now divide by coverage per bag:
Number of bags = 60 ÷ 5 = 12 bags

Let me verify: 5 × 12 = 60, and 60 ÷ 5 = 12 ✓

Problem 6:
The perimeter of a rectangular field is 80 ft and its width is 10 ft. Find the area.

First, find the length using the perimeter formula:
Perimeter = 2 × (length + width)
80 = 2 × (length + 10)
80 = 2 × length + 20
80 - 20 = 2 × length
60 = 2 × length
length = 60 ÷ 2 = 30 ft

Now find the area:
Area = length × width
Area = 30 × 10 = 300 square feet

Let me verify:
- Perimeter check: 2 × (30 + 10) = 2 × 40 = 80 ✓
- Area: 30 × 10 = 300 ✓

Final Answer:
1. 12 m
2. 105 square meters
3. 144 square feet
4. 42 ft
5. 12 bags
6. 300 square feet